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RISK AND REGULATION GIORGIO SZEGÖ University of
Rome La Sapienza and Università della Svizzera
Italiana, Lugano International Workshop on Risk
and Regulation Collegium Budapest Budapest,
Sept. 11-13, 2003
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CONTENTS

• RISK DEFINITION, MEASURES AND EVOLUTION
• REGULATION, MOTIVATIONS AND FASHIONS
• PROPOSALS
• 
  
  

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RISK DEFINITION, MEASURES AND EVOLUTIONWHAT IS
RISK?

• Objective, or subjective?
• Is it connected with an (economic) decision. See
  Arrow (Theory of Risk Bearing)
• Is it unavoidable (actuarial risk)?
• Markowitz theory separates the identification of
  the objective assets risk levels from the
  construction of the subjective utility
  function.
• Does subjective attitude toward risk affect the
  identification of the assets risk levels? Are
  spectral measures the answer?

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Qualitative properties of risk

• Uncertainty?
• Probability of loss or of undesirable events?
• These events can either be predictable or
• unpredictable, can be diversifiable and/or
• controllable, they can also be extreme.

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REGULATORY RISK CLASSIFICATIONS

• By impact.
• limited,
• systemic i.e. affecting all parties.
• systemic by contagion.
• By cathegory
• market risk,
• counterparty (credit) risk,
• operational risk.
• By source
• concentration,
• political,
• exchange,
• legal,
• fiscal, etc.

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Finance the 3 revolutions.

• 1952-56 Mean-Variance
• 1969-73 Continuous-time models
• 1999-03 Risk measures

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WHAT IS A MEASURE?

• Hopefully a non-negative real number!
• FOR INSTANCE, DISTANCES BETWEEN POINTS.
• The distance between any two points is 0 if and
  only if they coincide.
• The distance between any two points does not
  depends on their order.
• Given three points, the distance between any pair
  cannot be larger than the sum of the distances
  between the other two.
• To try to measure distances without these
  restrictions is equivalent to measuring distances
  with a rubber band!

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MANY FUNCTIONS ARE OK!

• Different functions can be used to measure
  distances
• In the space of ordered n-tuples of numbers
• ?o(x,y) max ?o(x,y)?yk - xk 1 ? k ? n
• as well as
• ?(x,y) ?? (yk xk)2½ (Euclidean distance)
• can measure the distance between any two points.
• CHOOSE THE ONE YOU LIKE MOST. THEY BOTH PERFORM
  THE DESIRED TASK!

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HOW TO BE A GOOD RISK MEASURE

• Risk measures associate to any multivariate
  distribution F a nonnegative real number.
• The functional F ? R must be restricted,
  like in the case of distances, utility functions
  or dynamical systems!
• In order to be a risk measure a functional F
  be coherent i.e. satisfy the following four
  conditions.

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RISK MEASURES

• For all random variables X, Y ? F, a risk
  measure
• ? F ? R must satisfy four conditions
• Positive homogeneity ?(?X) ? ??(X) for all
  positive real numbers ?.
• Subadditivity ?(X Y) ? ?(X) ?(Y).
• It can be proved that any positively
  homogeneous functional ?, is subadditive if and
  only if it is convex.
• Monotonicity X ? Y implies ?(X) ? ?(Y),
• Transitional invariance ?(X ?r0) ? ?(X) - ?
  for all real numbers ?, and risk free rates r0.
  
• 
  

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WHAT DO YOU WANT FROM A RISK MEASURE?

• FIRST COHERENCE AND REPEATIBILITY
• WITHIN THE SAME MEASURE! OK. DONE!
• CHOOSE YOUR OWN COHERENT MEASURE
• SECOND POSSIBILITY OF COMPARING RESULTS
  OBTAINED FROM DIFFERENT MEASURES NO WAY!.
• The only result is that a riskless event has
  a zero risk level for all possible risk
  measures.
• REGULATORY PROBLEMSjust too bad.
• 
  

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HOW RISK HAS BEEN MEASURED

• Expected returns adjusted to risk level.
• In 1952 Markowitz introduced multivariate
  distributions in finance, and showed that
  diversification decreases risk level.
• Risk (uncertainty) is measured via variance.
• Dependence is measured via (linear) correlation.
  
• 1994 The VaRmania.
• 1999 Introduction of proper Risk Measures
  

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WHEN CAN LINEAR CORRELATION BE USED?

• Only if the joint distributions are elliptic,
  i.e. if their equi-density surfaces are
  ellipsoids, like in the case of normal
  distributions or of t-distributions with finite
  variance.
• Symmetric distributions may not be elliptic. Most
  distributions of credit and high yield assets are
  not even symmetric.

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LINEAR CORRELATION FOR NON-ELLIPTIC DISTRIBUTIONS

• The linear correlation coefficient, if used in
  the case of non-elliptic distributions, may lead
  to incorrect results.
• The concept of incorrect must however be
  specified, since it requires an agreement on a
  correct co-dependence measure.
• In absence of such a measure one can compare
  numerical results achieved via simulations.
• Simulations show that a variance-covariance model
  for non-elliptic distributions severely
  underestimates potential losses.

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LINEAR CORRELATION MAY NOT EXPLAIN CO-DEPENDENCE!

• Comparing two different distributions (one normal
  and one Gumbel) with the same linear correlation
  coefficient, in the vast majority of cases the
  two results agree. Most of the points of
  disagreement lay in the upper right corner of the
  distribution, corresponding to extreme losses.
• It may not be always possible to measure
  co-dependence by a nonnegative real number!
• SourceEmbrechts, McNeil, and Straumann, 1999

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ENTER VALUE AT RISK

• In 1994 the concept of Value at Risk, VaR, was
  introduced with drums and cymbals with the
  precise task of answering to the following very
  relevant and precise questions
• How much one can expect to lose in on day, week,
  year,with a given probability?
• What is the percentage of the value of the
  investment that is at risk?
• Regulators fell in love with this easy-to-grasp
  concept and started misusing il!
• Ref. J.P. Morgan, 1994, see also Phelan, 1995.

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DEFINITION OF VAR

• VaRk is the k-percentile of the loss
  distribution, i.e. it is the smallest value such
  that the probability that loss exceeds or equals
  this value is bigger or equal to k, 0ltklt1. Thus
  VaRk is the maximum loss in a specified period
  with confidence level k.
• Formally
• VaRk ? F-1X(k)
• F-1X is the inverse of the distribution
  function FX.
• The distribution function FX is often
  referred to as the Profit and Loss distribution
  function.

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VAR MAY NOT EXIST!

• While VaR sounds like a great idea, when the
  distribution is multimodal, for some values of
  k,VaRk is not even defined. Indeed in this case
  the inverse of FX(k) does not exist and the
  inverse image of FX(k) is not even connected!
• In order to overcome this difficulty, VaR is
  defined as the lowest number belonging to the set
  F-1X(k), or as the k-quantile of the generalized
  inverse of FX, i.e.
• VaRk inf xFX(x)? k
• Keeping this caveat in mind, VaR could be used,
  albeit only in the case of the original question.
  The computational difficulties are not
  irrelevant.

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VAR IS NOT A RISK MEASURE

• VaR is not subadditive, i.e. it is not true that
  
• VaRk(P1 P2 ) ? VaRk (P1 ) VaRk (P2)
• This is like measuring distances with a rubber
  band!
• VaRk discourages diversification! This is like
  saying that a large bank is more risky than two
  smaller banks holding he same assets. The hell
  with portfolio risk reduction!
• Only when the joint distribution of returns is
  elliptic VaR is a risk measure. In this case a
  VaR-minimising portfolio the coincides with
  variance-minimising portfolio.
• Thus VaRk, that was introduced with the aim of
  measuring risk for weird distributions, can then
  be used only when the computationally simpler
  variance can be used.
  
  

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ENTHUSIASTIC ACCEPTANCE OF NEW RESULTSNO, GUT
REFUSALS

• resistance to innovation from a good part of the
  academic establishment, and from the conservative
  regulatory groups complete defence of the
  cultural investment in obsolete and methods that
  proved to be wrong!
• refusal even to be informed.
• The supervisory groups of central banks
  isolate themselves from the research and
  statistical department of the same institution!
  
  

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REGULATION, MOTIVATIONS AND FASHIONSWhy must
banks be regulated?

• WHO? WHAT?Which intermediaries and markets
  should be controlled.
• WHY?Motivations of regulation, i.e. a
  market-constraining public intervantion
• HOW?How to control.
• COSTS-BENFITS of regulatory intervantions.

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WHY AN AD-HOC REGULATION?

• Public Interest
• and subordinate to that
• Market inefficiency and consequent
• lack of self-discipline
• Insufficient protection from the core
• of law.

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PUBLIC INTEREST

• Economic Interest
• Can be measured by the costs associated with the
  lack of an efficient regulation and supervision,
  and by the consequent disruption of the
  activities of the subject
• Ethical Interest
• Protection of the weaker part of the users of
  financial services (the widows and the orphans)

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AIMS OF FINANCIAL REGULATION

• DAMAGE PREVENTION and/or CONTAINMENT
• guaranty the economic functions
• consumer protection
• systemic risk control
• guaranty market efficiency, fairness,
  transparency
• containment of possible direct government losses

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Regulatory Options

• Structural
• Institutional
• Functional
• Institutional-functional
• Prudential, SEIR (Early Intervention and
  Resolution)
• Market-enhancing.

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Why prudential regulation?

• Until the late 80 banks were controlled by
  structural regulation,
•     advances in telecommunications,
•     the introduction of derivatives,
• regulatory and fiscal arbitrage,
• forced its dismissal in favour of prudential
  regulation, aimed at
•     enhancing internal controls,
•     establishing an early warning system,
•     reducing taxpayer costs in case of default.
• It was implemented via capital requirements (1987
  UK-USA
• Capital accord, 1988 Basle accord, signed by 12
  countries,
• Group of 10 plus Luxembourg Switzerland)
•  

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1988 Capital Harmonization Accord.

• YOU MUST SATISFY THE FOLLOWING RISK-ADJUSTED
  CAPITAL REQUIREMENTS (NO DEFINITION OF RISK
  PROVIDED)
• (Own Funds)/(0.0 Sovreigns 0.2 Interbank 0.5
  Mortgages 1.0 Loans) gt 8
•  
• Own Funds Equity (Tier 1) Subordinated Debt
  (Tier 2)
• Equity gt Subordinated Debt
• EC Directives 89/299 and 89/647
• FDICIA 1992

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Why to Control Capital Level?(In spite of MM)

• Banks are informationally segregated,
• thus
• They are not exposed to market-discipline
• through the increase of the cost of debt with
  the degree of leverage
• No reason for risk-adjusted!

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Have Capital Requirements been Effective?

• No
• not always good indicators of financial
  conditions
• Swedish banks before the fall in 1992, 9.3
• Bank of Naples, 1994, 9.98
• Very Inaccurate
• Basel 5.304 5.304
  5.304
• Credit Metric 2.264 11.336
  2.941
• Very High Cost of Compliance

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Why to change?

• Official Critiques 1998-99 also from the
  Committee.
• No incentives for risk mitigation
• Disregard of maturity of claims
• Unwanted Consequences (We warned you!!!!)
• Excessive cost of credit to small business
• Increase in overall risk (Blum, JBF, 23, 1999)
• Regulatory arbitrages (Jones, JBF, 24, 2000)
• Inefficient cap allocation (BHS, JBF, 19, 1995)
• Credit crunch (Basel, WP N1, April 1999)
• Signal distortion in equity issues (Szego, 1993)

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Revision Process, alias a Path to Hell

• 1998, September, Framework for Internal Control
  System in Banking Organization
• 2001, January, The New Basel Capital Accord,
  Consultative Paper.
• 2003, The New Basel Capital Accord Consultative
  Paper, Comments due by July 2003
• What happened from 98 to 01? Lobbying!

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Framework for Internal Control System in Banking
Organization, 1998

• Safe and sound bank management is based on an
  efficient internal control system and on
• Management oversight and control culture
• Risk recognition and assessment
• Control activities and segregation of duties
• Information and communication
• Monitoring activities, correcting deficiencies
• Evaluation of internal control systems by
  supervisory authorities

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The proposal of 2001 is based on three pillows
(sorry, pillars)

• Minimal capital requirements 79.999
• Market discipline 15
• Prudential supervision 5
• and..
• Staff qualification
  0.001

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Whats new in basel 2?

• Good rating allows a discount on capital req.
• Internal rating procedures are allowed, if
  validated by supervisory authorities within a
  precise (wrong) framework.
• Concepts like DP and LGD play a major role.
• Risk must be measured by VaR
• Operational i.e. the risk of direct or indirect
  loss resulting from inadequate or failed internal
  processes, people and systems or from external
  events is taken into account.

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Dire effects of Basel II

• NO (very small) diversification bonus.
• NO maturity accounting
• NO control of bank size
• No penalization for exposure size
• Adopts VaR as a risk measure encouraging
  cheating.
• Enhances systemic risk by uniformizing behavours
• Requires very long data time series
• Favours large banks
• Memo the largest bank losses are due to loan
  concentration!!

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NEW PROPOSALS

• Advanced and more efficient market-discipline-enha
  ncing methods, like
• secondary market of loans
• continuous issues of subordinated debts